A design problem in many signal processing applications is to perform a given task or algorithm on a signal while introducing as little delay as possible. This delay is usually characterized by a measure known as group delay, defined as the negative rate of change of the total introduced phase shift with respect to angular frequency, −dθ/dω. A filter or system that introduces a constant group delay with respect to frequency is said to have linear phase. A filter or system with non-linear phase introduces variable delay with frequency (A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Englewood Cliffs, N.J.: Prentice-Hall Inc., 1989).
The importance of group delay depends on application, but is particularly critical in the design of audio devices, such as telephones, mobile phones, headsets, hearing aids, and cochlear implants. Introduction of additional signal path delay in these devices can have a significant impact on performance and usability. Specific problems can include:                increased perceivable echo from network or acoustic sources;        reduced perceptual coherence between user's own voice and side-tone or assisted listening path;        reduced perceptual coherence between listening cues & other sensory (e.g. visual) cues;        reduced control and integrity of delay differences in binaural listening;        reduced opportunity to avoid other perceptual problems, such as the occlusion effect (as described in J. Agnew and J. M. Thornton, Just Noticeable and Objectionable Group Delays in Digital Hearing Aids, Journal of the American Academy of Audiology, no. 11, pp. 330-336, 2000, J. Groth and M. B. Søondergaard, Disturbance caused by varying propagation delay in non-occluding hearing aid fittings, International Journal of Audiology, no. 43, pp. 594-599, 2004, M. A. Stone and B. C. J. Moore, Tolerable Hearing-Aid Delays: IV. Effects on Subjective Disturbance During Speech Production by Hearing-Impaired Subjects, Ear & Hearing, no. 26, pp. 225-235, 2005);        increased likelihood of feedback or gain instability;        increased resource requirements for echo or feedback cancellation; and        reduced sound quality, intelligibility and clarity of communication.        
Telecommunication standards also mandate strict compliance to rigorous specifications on group delay and its related effects, in order to maintain quality of communication in the network (for example see IEEE Std 269-2002: Standard Methods for Measuring Transmission Performance of Analog and Digital Telephone Sets, Handsets, and Headsets, The Institute of Electrical and Electronics Engineers (IEEE), New York N.Y., 2002, ITU-T Recommendation P. 340: Transmission characteristics and speech quality parameters for hands-free terminals, International Telecommunication Union (ITU), May 2000, Telstra Specification TP TT404B51: Specification—Headset & Limiting Amplifier. Acoustic Protection. Telstra Corporation Limited, Issue 3.1, 11 Jun. 2001).
Many modern audio devices use multi-band, or transform domain, signal processing techniques to improve some aspect of performance, but often incur significant group delay in the process. A predominant class of multi-band techniques utilized in audio processing applications uses block processing, with a Fast Fourier Transform (FFT) analysis, and Inverse Fast Fourier Transform (IFFT) overlap-add synthesis, to analyze and process signals in frequency sub-bands. This type of technique is depicted in the generalized block diagram of FIG. 1. In FIG. 1 the processing path 100 takes an input signal x[n] which is buffered by buffer 102 and then windowed with an analysis window wa[n] at 104. FFT block 106 then produces a frequency domain input X[k], which is suitably processed by a multi-band/frequency domain processing block 108 to generate a frequency domain output Y[k]. The frequency domain output Y[k] is passed through IFFT block 110, windowed at 112 with a synthesis window ws[n], and passed through overlap-add and de-buffer block 114 to produce output y[n].
A significant proportion of the group delay incurred in the arrangement of FIG. 1 occurs because of the necessity to initially buffer the input signal at 102 to be suitable for subsequent block operations in the signal path such as windowing 104, FFT 106, and IFFT 110. At a minimum, the group delay t1(min) is equivalent to the sample period multiplied by the window block size or FFT length L, plus a constant, so that:t1(min)=LFFT/fs+tp 
where fs is the base sample rate in Hz, and tp is the additional latency required for the processor to perform the required operations to obtain the final output block y[n].
Several other multi-band processing structures have also been used in audio devices, some targeted specifically at reducing group delay. One such method applies a time domain filter bank using IIR or FIR filters in place of the FFT filter-bank structure applied in FIG. 1. This type of scheme is depicted in FIG. 2. The processing path 200 of FIG. 2 divides input x[n] into multiple paths, each of which is passed to a respective filterbank and downsample/decimation block 202 to produce multiple sub-band domain inputs X[k]. The sub-band domain inputs X[k] are subject to multi-band/frequency domain processing at 204 to produce sub-band domain outputs Y[k]. Following upsampling/interpolation at 206, the multiple paths are combined at 208 to produce an output y[n].
The reduced group delay in the scheme of FIG. 2 typically comes from avoiding the block processing and buffering requirements seen in the FFT filter-bank schemes. In theory the group delay of FIG. 2 can be very low, particularly if interpolation & decimation stages are not required, and minimum phase (minimum group delay) filters are used in the filter-bank 202. Minimum group delay t2(min) of FIG. 2 is:t2(min)=ttdf+tp 
where ttdf is the minimum delay in the time domain filterbank 202, and tp is again the additional latency required to process for realization of the final output y[n]. The scheme also has the advantage of flexibility in allowing more selective or non-uniform resolution filters in the filter-bank, for example to mimic the Bark scale, or to reflect critical bands in human hearing.
However the filter-bank design of FIG. 2 is sensitive to cross-over and phase matching requirements, and implementation is computationally expensive to achieve the sub-band resolution achieved using an FFT for example. Furthermore, additional decimation and interpolation filtering is needed if the core processing is to be performed at a lower sample rate appropriate to the sub-band bandwidth. This decimation and interpolation process incurs additional group delay, but is important for the computational efficiency of many algorithms that would be used for the core processing.
Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application.
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